GEAR: GEometry-motion Alternating Refinement for Articulated Object Modeling with Gaussian Splatting

Jialin Li; Bin Fu; Ruiping Wang; Xilin Chen

cs.CVApr 9, 2026

GEAR: GEometry-motion Alternating Refinement for Articulated Object Modeling with Gaussian Splatting

Authors: Jialin Li, Bin Fu, Ruiping Wang, Xilin Chen

Organizations: Key Laboratory of AI Safety of Chinese Academy of Sciences (CAS), Institute of Computing Technology, CAS, Beijing, 100190, China · University of Chinese Academy of Sciences, Beijing, 100049, China

Abstract

High-fidelity interactive digital assets are essential for embodied intelligence and robotic interaction, yet articulated objects remain challenging to reconstruct due to their complex structures and coupled geometry-motion relationships. Existing methods suffer from instability in geometry-motion joint optimization, while their generalization remains limited on complex multi-joint or out-of-distribution objects. To address these challenges, we propose GEAR, an EM-style alternating optimization framework that jointly models geometry and motion as interdependent components within a Gaussian Splatting representation. GEAR treats part segmentation as a latent variable and joint motion parameters as explicit variables, alternately refining them for improved convergence and geometric-motion consistency. To enhance part segmentation quality without sacrificing generalization, we leverage a vanilla 2D segmentation model to provide multi-view part priors, and employ a weakly supervised constraint to regularize the latent variable. Experiments on multiple benchmarks and our newly constructed dataset GEAR-Multi demonstrate that GEAR achieves state-of-the-art results in geometric reconstruction and motion parameters estimation, particularly on complex articulated objects with multiple movable parts.

Figures & tables

Figure 1: Articulated object modeling involves coupled optimization of geometry and motion. Motion analysis plays a key role in part reconstruction, while joint motion parameter estimation relies on accurate part segmentation. Unlike coupled and staged methods, GEAR utilizes alternating optimization to improve stability.

Figure 2: GEAR is an EM-style framework with three modules: Initialization, geometry modeling, and motion modeling. The key idea is the alternating optimization of geometry and motion, which enhances the stability and performance of articulated object modeling.

Figure 3: SAM Mask Aggregation module. Each fine-grained candidate region $S^{u}$ from SAM is assigned to the Gaussian part $M^{k}$ with the highest spatial overlap. All SAM regions assigned to the same part $k$ are then aggregated to form a coherent mask $F^{k}$ , serving as a weak supervision signal to refine $M^{k}$ .

Method	Simulated (Average)						Real (Average)
Method	Axis Ang	Axis Pos	Geo Dist	CD-s	CD-m	CD-w	Axis Ang	Axis Pos	Geo Dist	CD-s	CD-m	CD-w
Ditto	46.22	2.11	39.87	18.94	42.20	7.12	3.80	1.84	4.41	31.55	35.48	10.29
PARIS	6.23	1.04	41.71	7.18	39.76	5.47	22.39	0.34	1.36	48.56	455.24	43.17
DTA	0.13	0.02	0.13	2.45	1.66	1.79	7.86	0.59	1.00	6.67	15.95	5.53
ArtGS	0.02	0.00	0.02	2.63	0.67	2.15	2.78	0.47	0.99	2.29	3.47	2.26
Ours	0.02	0.00	0.02	1.99	0.70	1.87	3.50	0.38	1.18	2.60	8.35	2.99

Table 1: Quantitative comparison on the PARIS dataset [ 28 ] , averaged over 10 trials for both simulated and real objects with higher visibility. Lower (

\downarrow

) is better for all metrics. We highlight the best ( Bold with Top-1 ) and second-best ( Top-2 ) results. Baseline results for Ditto, PARIS, DTA, and ArtGS are sourced from [ 31 ] .

Object	Method	Axis Ang	Axis Pos	Geo Dist	CD-s	CD-m	CD-w
Table (4)	DTA	24.35	-	0.12	0.59	104.38	0.55
	ArtGS	1.16	-	0.00	0.74	3.53	0.74
	Ours	0.08	-	0.00	0.47	0.23	0.51
Table (5)	DTA	20.62	4.2	30.8	1.39	230.38	1.00
	ArtGS	0.04	0.00	0.01	1.22	3.09	1.16
	Ours	0.04	0.00	0.02	0.77	0.26	0.98

Table 2: Quantitative comparison on the ArtGS-Multi dataset [ 31 ] . Numbers in parentheses (e.g., Table (4)) indicate the count of dynamic parts. Results are reported as the mean over 3 trials. Lower (

\downarrow

) is better for all metrics, Bold indicates the best results. Axis Pos. is omitted for “Table (4)” which contains only prismatic joints. Baseline results for DTA and ArtGS are sourced from [ 31 ] .

Figure 4: Qualitative results on complex multi-joint articulated objects. Compared to ArtGS [ 31 ] , Our method exhibits geometric reconstruction quality and more accurate motion parameter estimation.

	Storage_47648						Storage_45271
Method	Axis Ang	Axis Pos	Geo Dist	CD-s	CD-m	CD-w	Axis Ang	Axis Pos	Geo Dist	CD-s	CD-m	CD-w
Full	0.07	0.01	0.10	0.61	0.32	0.60	0.03	0.00	0.03	0.50	0.10	3.92
2DGS $\to$ 3DGS	0.07	0.00	0.03	0.66	0.70	0.77	1.02	0.40	2.94	0.46	0.21	0.98
w/o self_loss	22.67	0.94	30.38	1.48	F	2.42	35.83	475.96	24.91	11.78	F	6.16
w/o knn_loss	0.05	0.00	0.09	0.52	20.93	0.59	0.02	0.00	0.02	0.49	32.38	0.90
staged optimization	15.28	0.66	13.36	2.07	F	1.43	29.61	1.29	7.04	11.72	24.34	1.05

Table 4: Ablation study on GEAR’s components. We conduct experiments on two representative and highly complex 7-part objects (Storage_47648 and Storage_45271), lower (

\downarrow

) is better for all metrics.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1 : Visualization of Initialization and Convergence. Top row: The coarse point clouds derived from the voxel-based initialization module. Colors indicate different initialized parts. Bottom row: The final high-fidelity reconstruction after GEAR optimization. The comparison highlights that while the coarse module produces rough and discretized structures, it successfully captures the topological structure, guiding GEAR to converge to a photorealistic and geometrically accurate result.

Category	Parameter	Value
Initialization	Voxel Size $v$	0.1 / 0.01 ∗
Initialization	Morphological Dilation Radius	1
Training Loop	Total Iterations	30,000
	E-step Interval	500
	M-step Interval	500
	KNN Gaussian Neighbors $\mathcal{N}$	3

Appendix

Table S1: Hyperparameters setting of GEAR.

Object	Parts	Initialization	training	Total Time
Box	5	13	35	48
Bucket	3	13	27	40
Clock	3	9	16	25
Door	3	12	17	29
EyeGlasses	3	10	24	34
Faucet	3	9	20	29

Appendix

Table S2 : Runtime Breakdown on GEAR-Multi. Time is measured in minutes. The total computational cost scales reasonably with the number of movable parts.

Method	Time (min) $\downarrow$	Axis Ang $\downarrow$	Axis Pos $\downarrow$	Geo Dist $\downarrow$	CD-s $\downarrow$	CD-m $\downarrow$	CD-w $\downarrow$
ArtGS [ 31 ]	14.0	8.82	141.45	12.83	0.90	115.70	1.12
Ours ∗ (Fast)	11.4	0.30	0.01	0.34	0.99	3.00	0.95
Ours (Full)	34.0	0.09	0.09	0.08	0.86	0.71	1.13

Appendix

Table S3 : Performance of the Fast Version on GEAR-Multi (Average). Our fast version ( Ours ∗ ) outperforms ArtGS in runtime while delivering substantially higher accuracy.

Method	Axis Ang $\downarrow$	Axis Pos $\downarrow$	Geo Dist $\downarrow$	CD-s $\downarrow$	CD-m $\downarrow$	CD-w $\downarrow$
Ours (Joint)	0.11	0.00	0.32	2.32	2.19	1.93
Ours (EM)	0.02	0.00	0.02	1.99	0.70	1.87

Appendix

Table S4 : Alternating vs. Joint Optimization on PARIS dataset. The results indicate that GEAR works reasonably well under joint optimization, while EM strategy behaves better.

Method	Axis Ang $\downarrow$	Axis Pos $\downarrow$	Geo Dist $\downarrow$	CD-s $\downarrow$	CD-m $\downarrow$	CD-w $\downarrow$
ArtGS	8.82	141.45	12.83	0.90	115.70	1.12
ArtGS + EM	7.77	0.86	11.33	0.80	27.46	1.37

Appendix

Table S5 : Plugin Capability. Applying EM framework (15k joint pre-training followed by 5k EM alternating refinement) to ArtGS [ 31 ] on the GEAR-Multi dataset reduces modeling errors.

Method	Storage_47648						Storage_45271
Method	Axis Ang $\downarrow$	Axis Pos $\downarrow$	Geo Dist $\downarrow$	CD-s $\downarrow$	CD-m $\downarrow$	CD-w $\downarrow$	Axis Ang $\downarrow$	Axis Pos $\downarrow$	Geo Dist $\downarrow$	CD-s $\downarrow$	CD-m $\downarrow$	CD-w $\downarrow$
ArtGS	0.14	0.02	0.62	0.67	3.70	0.70	9.33	1268.83	5.85	1.27	102.33	1.74
Ours-50	0.06	0.01	0.13	0.53	0.23	0.60	0.03	0.00	0.07	0.49	0.17	0.89
Ours-250	0.13	0.01	0.15	0.57	0.22	0.59	0.02	0.00	0.05	0.55	0.17	0.91
Ours-500 (Default)	0.07	0.01	0.10	0.61	0.32	0.60	0.03	0.00	0.03	0.50	0.10	3.92
Ours-2000	0.05	0.01	0.12	0.54	0.26	0.60	0.03	0.00	0.03	0.43	0.16	0.91

Appendix

Table S6 : Robustness Analysis of the EM Alternating Interval. Evaluated on two complex 7-part objects. GEAR maintains stable, high-quality convergence across a broad range of interval settings (50 to 2000). Degeneration only occurs when the interval is excessively large (

\geq 3000

), mimicking the failure mode of staged optimization.

Figure S2 : Failure Cases of SAM. Visualizations of flawed 2D masks, including over-segmentation (left) and under-segmentation (right), which serve as the challenging initial priors for our framework.

Object	Axis Ang $\downarrow$	Axis Pos $\downarrow$	Geo Dist $\downarrow$	CD-s $\downarrow$	CD-m $\downarrow$	CD-w $\downarrow$
Window_102985	0.06	-	0.00	0.77	2.10	0.68
Refrigerator_10685	0.00	0.00	0.02	0.52	0.10	0.53

Appendix

Table S7 : Performance under Flawed 2D Priors. GEAR maintains high accuracy despite being initialized with the erroneous masks shown in Fig. S2 .

Figure S3 : Qualitative comparison on the ArtGS-Multi dataset. We visualize all reconstruction results across two states. The columns show the results from the ArtGS baseline, Ours, and the Ground Truth (GT). As highlighted in the visualizations (e.g., Oven 101918 and Table 31249 ), ArtGS struggles to distinguish spatially adjacent parts, leading to fused segmentation. In contrast, GEAR accurately disentangles these components and estimates precise motion axes.

Figure S4 : Qualitative comparison on the GEAR-Multi dataset. We present results on all 10 objects with diverse categories and topological structures. GEAR demonstrates robustness in handling objects with thin structures and small movable parts (e.g., Bucket 100481 , Knife 101068 ), whereas ArtGS often fails to capture these fine-grained geometries or generates noisy artifacts.

Figure S5 : Novel Joint Motion Synthesis. We render the articulated object at intermediate states $t=\{0,0.2,0.4,0.6,0.8,1\}$ . GEAR (Bottom) preserves the geometry of the door and the contents inside the fridge consistently throughout the motion trajectory, whereas the baseline (Top) suffers from geometric distortion and blurring.

Figure S6 : Qualitative results on real-world objects. The top two rows display single-joint objects from the PARIS dataset. The third row shows a multi-joint cabinet from the ArtGS dataset, and the bottom row depicts a printer captured in our lab. While ArtGS achieves comparable results on simple single-joint objects, it fails to reconstruct the structural details of complex multi-joint objects, leading to noisy artifacts. GEAR consistently delivers high-fidelity reconstruction and accurate part segmentation across all sources.

Figure S7 : Spatial Ambiguity in Initialization. Top: When two movable parts are spatially adjacent with no gap (parallel drawers), our coarse module may fail to separate them, initializing them as a single part. Bottom: When parts are spatially staggered (offset drawers), the module successfully identifies distinct components.

Figure S8 : Misclassification in Extreme Motion. For a safe box door rotating 180 degrees, the large displacement and lack of intermediate visual cues lead the model to misclassify the revolute joint as a prismatic joint (visualized by the incorrect linear motion arrow).

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